The maximum height of the boulder can be found by taking the derivative of the given function h(t) and setting it equal to 0 to find the critical points.
Given: h(t) = -5t^2 + 92t + 16
Taking the derivative:
h'(t) = -10t + 92
Setting h'(t) = 0 and solving for t:
-10t + 92 = 0
-10t = -92
t = 9.2
So, it takes 9.2 seconds for the boulder to reach its maximum height.
To find the maximum height, substitute t = 9.2 back into the original function:
h(9.2) = -5(9.2)^2 + 92(9.2) + 16
h(9.2) = -5(84.64) + 844.8 + 16
h(9.2) = -423.2 + 844.8 + 16
h(9.2) = 437.6
Rounded to the nearest hundredth, the boulder's maximum height is 437.6 meters.
Therefore, the correct answer is: Reaches a maximum height of 437.6 meters in 9.2 seconds.
A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h = –5t2+ 92t + 16. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
(1 point)
Responses solve it and tell me why
Reaches a maximum height of 16.00 meters in 18.4 seconds.
Reaches a maximum height of 16.00 meters in 18.4 seconds.
Reaches a maximum height of 18.57 meters in 9.2 seconds.
Reaches a maximum height of 18.57 meters in 9.2 seconds.
Reaches a maximum height of 37.14 meters in 18.4 seconds.
Reaches a maximum height of 37.14 meters in 18.4 seconds.
Reaches a maximum height of 439.20 meters in 9.2 seconds.
1 answer
1 answer